The Global Theory Of Minimal Surfaces In Flat Spaces
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The Global Theory Of Minimal Surfaces In Flat Spaces
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Author : W.H. III Meeks
language : en
Publisher: Springer
Release Date : 2004-10-11
The Global Theory Of Minimal Surfaces In Flat Spaces written by W.H. III Meeks and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-11 with Mathematics categories.
In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.
The Global Theory Of Minimal Surfaces In Flat Spaces
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Author : Centro Internazionale Matematico Estivo. Session
language : en
Publisher:
Release Date : 2002
The Global Theory Of Minimal Surfaces In Flat Spaces written by Centro Internazionale Matematico Estivo. Session and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
The Global Theory Of Minimal Surfaces In Flat Spaces
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Author : William H. III. Meeks
language : en
Publisher:
Release Date : 2004
The Global Theory Of Minimal Surfaces In Flat Spaces written by William H. III. Meeks and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Global Analysis Of Minimal Surfaces
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Author : Ulrich Dierkes
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-16
Global Analysis Of Minimal Surfaces written by Ulrich Dierkes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-16 with Mathematics categories.
Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of "edge-crawling" along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a "global theory of minimal surfaces" as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmüller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau ́s problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented.
Minimal Surfaces
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Author : A. T. Fomenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Minimal Surfaces written by A. T. Fomenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Minimal surfaces categories.
This book contains recent results from a group focusing on minimal surfaces in the Moscow State University seminar on modern geometrical methods, headed by A. V. Bolsinov, A. T. Fomenko, and V. V. Trofimov. The papers collected here fall into three areas: one-dimensional minimal graphs on Riemannian surfaces and the Steiner problem, two-dimensional minimal surfaces and surfaces of constant mean curvature in three-dimensional Euclidean space, and multidimensional globally minimal and harmonic surfaces in Riemannian manifolds. The volume opens with an exposition of several important problems in the modern theory of minimal surfaces that will be of interest to newcomers to the field. Prepared with attention to clarity and accessibility, these papers will appeal to mathematicians, physicists, and other researchers interested in the application of geometrical methods to specific problems.
A Survey On Classical Minimal Surface Theory
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Author : William Meeks
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
A Survey On Classical Minimal Surface Theory written by William Meeks and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Meeks and Pérez extend their 2011 survey article "The classical theory of Minimal surfaces" in the Bulletin of the American Mathematical Society to include other recent research results. Their topics include minimal surfaces with finite topology and more than one end, limits of embedded minimal surfaces without local area or curvature bounds, conformal structure of minimal surfaces, embedded minimal surfaces of finite genus, topological aspects of minimal surfaces, and Calabi-Yau problems. There is no index. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com).
A Survey Of Minimal Surfaces
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Author : Robert Osserman
language : en
Publisher: Courier Corporation
Release Date : 2013-12-10
A Survey Of Minimal Surfaces written by Robert Osserman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-10 with Mathematics categories.
Newly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein’s theorem, much more, including such recent developments as new work on Plateau’s problem and on isoperimetric inequalities. Clear, comprehensive examination provides profound insights into crucial area of pure mathematics. 1986 edition. Index.
Minimal Surfaces From A Complex Analytic Viewpoint
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Author : Antonio Alarcón
language : en
Publisher: Springer Nature
Release Date : 2021-03-10
Minimal Surfaces From A Complex Analytic Viewpoint written by Antonio Alarcón and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.
This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.
Minimal Surfaces From A Complex Analytic Viewpoint
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Author : Antonio Alarcón
language : en
Publisher:
Release Date : 2021
Minimal Surfaces From A Complex Analytic Viewpoint written by Antonio Alarcón and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann-Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi-Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.
Arithmetic Theory Of Elliptic Curves
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Author : J. Coates
language : en
Publisher: Springer
Release Date : 2006-11-14
Arithmetic Theory Of Elliptic Curves written by J. Coates and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.